Our data set contains many variables related to course-specific performance and overall GPA. In looking at the grades for the course, the teacher sees that students in one section performed much better on the third quiz than the students in the other two sections of the course. The teacher is concerned about why students taking identical quizzes in each section are performing so differently. She hypothesizes that one section might comprise students with higher overall GPAs and therefore are stronger students than those in the other two sections. To see if removing the variance in quiz 3 that is explained by the GPA of the students, you will perform a one-way ANCOVA using the variables quiz 3, GPA, and section.

Instructions

1. Briefly describe the goal of your analysis.
   • Specify the variables used in this analysis (independent, covariate, and dependent) and the scale of measurement of each variable.
   • State the sample size (N) and the alpha level you will use (.05 unless otherwise specified).
   • Explain why the analysis is a good choice based on the nature of your variables.
2. Specify a research question and articulate a null hypothesis and alternative hypothesis. Specify the alpha level.
3. Articulate and test the assumptions of ANCOVA.
   • Paste the histogram output for Quiz 3 and discuss your visual interpretations.
   • Paste descriptives output showing skewness and kurtosis values for Quiz 3 and interpret them.
   • Paste the output for the Shapiro-Wilk test of Quiz 3 and interpret the results.
   • Report the results of the Levene test and interpret it.
   • Present the results of the test of homogeneity of regression slopes.
   • Explain whether the assumptions of ANCOVA are met. If assumptions are not met, discuss how to ameliorate violations of the assumptions.
4. Paste the output of the means plot and provide an interpretation.
   • Also, report the means and standard deviations of Quiz 3 and GPA for each level of the section variable.
   • Paste the ANOVA output and report the results of the F test. Include the following:
     • Degrees of freedom.
     • Fvalues.
     • pvalues.
     • Interpretation of the effect size.
     • Interpret statistical results against the null hypothesis and state whether it is accepted or rejected.
5. Provide a summary of your analysis and the conclusions drawn.
   • Discuss whether the removal of the variance in Quiz 3 that was explained by GPA influences the relationship between Quiz 3 and the section.
   • Analyze the strengths and limitations of the statistical test.
   • Provide any possible alternate explanations for the findings and potential areas for future exploration.

Additional Requirements

• Written communication: This should be free of errors that detract from the overall message.